We compare the direct GREG estimators \(\hat{\theta }_i^{\mathrm {d}}\)  given in (REF ), the GREG-synthetic estimators \(\hat{\theta }_i^{\mathrm {S}}\)  from (REF ), their first-step compositions (REF ), and the composite estimators \(\hat{\theta }_i^{\mathrm {Cb}}\)  by (REF ) with EBLUPs based on the basic unit-level model [1]}. We calculate these EBLUPs applying the function eblupBHF from R package sae [2]}. To get parametric bootstrap MSE estimates for the predictors, we use the function pbmseBHF from the same package. We compare that MSE estimation with MSE estimators (REF ) applied to compositions (REF ) and (REF ). The results for the proportions of the unemployed and employed are in Tables REF  and REF , respectively.
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